Adiabatic process/ work done

1. The problem statement, all variables and given/known data
During an adiabatic process, the temperature of 5.50 moles of a monatomic idea gas drops from 495 C to 215 C. For this gas, find (a) the work it does, (b) the heat it exchanges with its surroundings, and (c) the change in its internal energy

2. Relevant equations
I know work is P(delta V)
PV1=nRT1 and
PV2=nRT2 so if I subtract to get the change,
P(deltaV)=nR(delta T)
P(deltaV)=5.50(8.31)(280)
P(deltaV)= 12797.4 Joules.
But my text book says this isn't the answer.
Where did I go wrong?

I know the answer for b is zero, since that's the definition of an adiabatic process

1. The problem statement, all variables and given/known data
During an adiabatic process, the temperature of 5.50 moles of a monatomic idea gas drops from 495 C to 215 C. For this gas, find (a) the work it does, (b) the heat it exchanges with its surroundings, and (c) the change in its internal energy

Do c) first. You are given the initial and final temperatures so you can determine the change in internal energy. How is the work done related to the change in internal energy if dQ = 0?

The energy of an ideal gas depends only on its temperature, by the relationship

[tex]\Delta U=c_Vn\Delta T[/tex]

The molar heat capacity [itex]c_V[/itex] is [itex]\frac{3}{2}R[/itex] for a monatomic gas. The 3/2 factor can be derived (from statistical mechanics), but the derivation is very complex compared to what you're studying now.